Let $f : X \to Y$ be a proper morphism of schemes i.e. universally closed, finite type, separated. Then the valuative criteria states that it is iff the condition that given a commutative diagram of maps from a valuation ring $specR \to Y$ and its fraction field $specK \to X$ there exists a unique lift $specR \to X$.
Now in the valuative criteria for proper maps between Deligne Mumford stacks (following Jarod Alper's notes available online and on YouTube) he says the criteria is there is a lift after possibly an extension $specR' \to specR$ to some other valuation ring and its fraction field.
So this should obviously hold at the level of schemes too.
Question : For schemes if there is a lift after extension to a new valuation ring, why is there an extension for the original valuation ring?